## Notre Dame Journal of Formal Logic

### Forking and Dividing in Henson Graphs

Gabriel Conant

#### Abstract

For $n\geq3$, define $T_{n}$ to be the theory of the generic $K_{n}$-free graph, where $K_{n}$ is the complete graph on $n$ vertices. We prove a graph-theoretic characterization of dividing in $T_{n}$ and use it to show that forking and dividing are the same for complete types. We then give an example of a forking and nondividing formula. Altogether, $T_{n}$ provides a counterexample to a question of Chernikov and Kaplan.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 58, Number 4 (2017), 555-566.

Dates
Accepted: 10 July 2015
First available in Project Euclid: 6 June 2017

https://projecteuclid.org/euclid.ndjfl/1496736030

Digital Object Identifier
doi:10.1215/00294527-2017-0016

Mathematical Reviews number (MathSciNet)
MR3707651

Zentralblatt MATH identifier
06803187

#### Citation

Conant, Gabriel. Forking and Dividing in Henson Graphs. Notre Dame J. Formal Logic 58 (2017), no. 4, 555--566. doi:10.1215/00294527-2017-0016. https://projecteuclid.org/euclid.ndjfl/1496736030

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